Router DNS issue with Adguard installed

In the first post there is a WAN Dns script that will set your WAN to ignore upstream DHCP DNS settings and force set your own. That will at least ensure your router can do DNS properly.

However that doesn't solve why your router fails to get dns after installing AGH.

Your clients obviously are getting the dhcp dns option 6 address for AGH. Your router should still be using its WAN DHCP supplied dns.